We were there last year to catch a couple of Brewer games. We stayed a mile north of the White House. A wide selection of nice places to grab dinner in that area. We were at the Capitol when Congress was in session, that was neat. But they're not in session now. They give tours, but I found it brief. Secure a tour pass online. Or go across the street and visit the offices of Wisconsin's two senators. Hang out at the National Mall, I preferred the late afternoon. People are getting off work, so there are softball games going on, maybe a rugby match. People jogging. The DC crowd skews young and lead active lives. Places to visit would be Arlington Cemetery or any of the galleries, all on the Metro. Trump Hotel, if inclined. I really didn't see any places to hang out around Nationals Park. The Metro drops off two blocks from the stadium. Most went straight to the train station after the game. On edit: the good places to eat are north of the White House, not the Capitol.